TY - JOUR
T1 - Boundedness of Commutators for Multilinear Marcinkiewicz Integrals with Generalized Campanato Functions on Generalized Morrey Spaces
AU - Ku , Fuli
JO - Journal of Mathematical Study
VL - 4
SP - 411
EP - 437
PY - 2023
DA - 2023/12
SN - 56
DO - http://doi.org/10.4208/jms.v56n4.23.07
UR - https://global-sci.org/intro/article_detail/jms/22316.html
KW - Multilinear, Marcinkiewicz integrals, commutators, generalized Campanato spaces, generalized Morrey spaces.
AB - <p style="text-align: justify;">This paper is devoted to exploring the mapping properties for the commutator $\mu_{Ω,\vec{b}}$ generated by multilinear Marcinkiewicz integral operators $\mu_Ω$ with a locally
integrable function $\vec{b}= (b_1,···,b_m)$ on the generalized Morrey spaces. $\mu_{Ω,\vec{b}}$ is bounded
from $L^{(p_1
,\varphi_1)} (\mathbb{R}^n
)×···×L^{(p_m,\varphi_m)} (\mathbb{R}^n)$ to $L ^{(q,\varphi)} (\mathbb{R}^n),$ where $L^{(p_i
,\varphi_i
)} (\mathbb{R}^n),$ $L^{(q,φ)} (\mathbb{R}^n)$ are
generalized Morrey spaces with certain variable growth condition, that $b_j(j=1,···,m)$ is a function in generalized Campanato spaces, which contain the BMO$(\mathbb{R}^n)$ and the
Lipschitz spaces ${\rm Lip}_α(\mathbb{R}^n) (0&lt;α≤1)$ as special examples.</p>